Related papers: A moonshine dialogue in mathematical physics
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
In this short paper, the results of the paper by Drab et al. (Eur. Phys. J. E (2022) 45:79) are described in the framework of wave mechanics and mathematical physics based on common understandings. The attention is focused on properties of…
A workshop using dance to introduce particle physics concepts to young children is presented. The workshop is realised in the dance studio, the children assume complete ownership of the activity and dance becomes the means to express ideas.…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…
This note is based on four lectures that I gave at the 10th Taiwan Nuclear Spring School held at Hualien, Taiwan in January 2002. It aims to correlate the old notion of Cheshire Cat Principle developed for elementary baryons to the modern…
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one…
Understanding and reasoning about physics is an important ability of intelligent agents. We develop the PHYRE benchmark for physical reasoning that contains a set of simple classical mechanics puzzles in a 2D physical environment. The…
In quantum mechanics, collisions between two particles are captured by a scattering matrix which describes the transfer from an initial entrance state to an outgoing final state. Analyticity of the elements of this $S$-matrix enables their…
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…
A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
In theories with (sets of) two large extra dimensions and supersymmetry in the bulk, the presence of non-supersymmetric brane defects naturally induces a logarithmic potential for the volume of the transverse dimensions. Since the logarithm…
We model two bosons in an optical lattice near a Feshbach or photoassociation resonance, focusing on the Bose-Hubbard model in one dimension. Whereas the usual atoms-only theory with a tunable scattering length yields one bound state for a…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
In the early fifties, the Belgian Prof. J. de Heinzelin discovered a bone in the region of a fishermen village called Ishango, at one of the farthest sources of the Nile, on the border of Congo and Uganda. The Heinzelin's Ishango bone has…
Tensors are fundamental in mathematics, computer science, and physics. Their study through algebraic geometry and representation theory has proved very fruitful in the context of algebraic complexity theory and quantum information. In…
Big-Bang cosmology and ideas for possible physics beyond the Standard Model of particle physics are introduced. The density budget of the Universe is audited, and the issues involved in calculating the baryon density from microphysics are…